Part 1 Discrete-time order-preserving dynamical systems: monotone iteration schemes
connecting orbits; stabilization
existence of stable fixed points
an example to stabilization - sublinear mappings
existence of unstable fixed points
prerequisites - the theorems of Krein-Rutman
instability for differentiable maps
continuous-time order-preserving dynamical systems.
Part 2 The linear periodic-parabolic eigenvalue problem: prerequisites - linear evolution equations of parabolic type in a Banach space
prerequisites - linear parabolic differential equations; the maximum principle; the periodic-parabolic eigenvalue problem; a one-parameter family of eigenvalue problems; the periodic-parabolic eigenvalue problem with respect to an indefinite weight function
estimates for the principal eigenvalue.
Part 3 The nonlinear periodic-parabolic problem: prerequisites - semilinear evolution equations of parabolic type in a Banach space
prerequisites - semilinear parabolic differential equations
the semilinear periodic-parabolic initial value problem
existence of stable periodic solutions
stability of periodic solutions
a general convergence result; convergence of solutions in a periodic-parabolic Neumann problem
bifurcation of periodic solutions
bifurcation of periodic solutions
bifurcation for concave and convex nonlinearities
the periodic-parabolic logistic equation
the periodic Fisher equation.
Part 4 The periodic Volterra-Lotka competition system with diffusion: a priori estimates for fixed points of S
the Volterra-Lotka system in the compressive case
extinction in the competition system
an unstable coexistence state.
Part 5 the periodic Volterra-Lotka predator-prey system with diffusion: nonlocal perturbation of the logistic equation
sufficiency for coexistence
extinction in the predator-prey system.
